1. Field of the Invention
This invention in general relates to methods for making metal stamping dies suitable for use in forming reflectors for use in photographic lighting apparatus and in particular to a method for making such dies for forming reflectors of the type having cross-sectional shapes in the form of polynomial curves.
2. Description of the Prior Art
The utilization of reflectors to intercept radiation emanating from a source and redirect that radiation in a controllable manner to make more efficient use of the available source radiation and achieve a preferred distribution in the intensity of illumination falling on a subject is a well-established practice in the photographic and optical arts.
In lighting apparatus utilizing reflectors, the reflector shape plays an important role, particularly when combined with small sources, in determining the overall area illuminated by the apparatus and the manner in which the illumination varies from one point to another over that area. For photographic lighting apparatus, it is desirable that point-to-point variation in illumination occur in a gradual or smooth manner over the area illuminated because any abrupt change in the intensity of the illumination from one point or area of a subject to another point or area is visually detectable in a photograph as a correspondingly abrupt change in picture density which is not related to actual changes in subject reflectivity as it should be.
Such abrupt changes in illumination could be seen in a picture as alternating light and dark bands across the picture area and are caused by reflector artifact related to the imaging properties of reflectors, how those properties operate to direct illumination over the area illuminated, and how the imaging properties, either by design or fabrication, change from one part of the reflector to another.
In general, the illumination of a point located, say in a plane normal to a lighting apparatus, due to the reflected component of the light from an apparatus depends on the reflectivity of the reflector surface, the size and location of the reflected image of the source, and the solid angle subtended by the image of the source as seen from the point. The size and location of the reflected image from the source, which in turn determine the solid angle subtended by the image of the source as seen from a point, depend on the local curvature of the reflector and how that curvature changes. If the shape of a reflector is such that the local curvature, and hence optical power, abruptly changes, there is a correspondingly abrupt change in the illumination between points or areas of the normal plane which derive their illumination from those portions of the reflector surface where the abrupt change in optical power occurs. Consequently, any reflector shape whose optical power or local radius of curvature does not change in a gradual manner will, depending on the degree of change, cause more or less abrupt changes in illumination from one point to another which are undesirable for photographic purposes.
In U S. Pat. No. 4,356,538 filed in the name of William T. Plummer on Aug. 4, 1980 and entitled "Photographic Lighting Apparatus" and in U.S. Pat. No. 4,355,350 filed in the name of John J. Mader on (mailed Aug. 28, 1980) and entitled "A Reflector For Use In An Artificial Lighting Device", there are described concave reflectors which do not cause abrupt changes in illumination and are therefore highly desirable for photographic lighting work. The reason why the above-noted reflectors do not cause abrupt changes in illumination is a consequence of their reflector shapes which are in the form of higher order polynomials whose first and second derivatives, which determine their radius of curvature and hence optical power, are mathematically continuous. Since the local optical power of these reflectors changes in a gradual manner, the point-to-point variation in illumination provided by these reflectors, when used in combination with a light source, also changes in a gradual manner.
The lighting performance of such polynomial reflectors obviously depends on how well the polynomial shape can be produced with a particular manufacturing process. Polynomial shapes of this sort are capable of being reproduced rather exactly with optical injection molding techniques for fabricating plastic lenses. A mold can be easily shaped by using electric discharge machining techniques to cut the mold and thereafter the mold can be polished to optical tolerances to fabricate a die which will rather precisely reproduce the polynomial shape. Afterwards, a plastic injection molded reflector part is easily provided with a reflector surface through conventional vacuum deposit techniques. However, because of the desirability for fabricating these reflectors from sheet metal and because of the economic benefit from metal stamping, it is a primary object of the present invention to provide a method by which metal stamping dies can be fabricated for forming such reflectors.
Another object of the present invention is to provide a method by which metal stamping dies can be fabricated to produce reflectors having a sufficient approximation of a polynomial shaped reflector so that reflectors formed thereby perform in apparently the same manner as would the precise polynomial shape of the reflector.
Other objects of the invention will, in part, be obvious and will, in part, appear hereinafter. The invention accordingly comprises the method possessing the sequence of steps which are exemplified in the following detailed disclosure.